More than 25 new compensations claims have been filed in domestic Italian courts against the German state over damages arising from Nazi atrocities. In many of the cases, Italian courts have ordered Germany to pay.
Germany is also seeking financial compensation from Italy "for any injury caused through violations of Germany's right to sovereign immunity."
Why did Germany file the case now?
The most pressing issue for Germany is a pending Italian court ruling on whether to force the sale of German-owned buildings.
The four properties include buildings in Rome that house the local offices of the German Archaeological Institute, the German Historical Institute, the cultural Goethe Institute and the German School of Rome.
Germany argues in its filing that "Italy has violated, and continues to violate, its obligation to respect Germany's sovereign immunity" by threatening to take the buildings to pay complaints filed by victims of Nazi crimes.
An Italian court said it would decide on May 25 whether to auction off the buildings.
Germany urged the ICJ to take measures to halt the auction of the properties while the larger case over WWII compensation claims is being considered.
No hearing has been scheduled, but one is expected within the next few weeks. Rulings in the ICJ typically take years to come through.
Nazi atrocities in Italy and the winding road of reparations
Germany and Italy have been locked in a legal dispute over WWII reparations for years.
In the ICJ's previous 2012 decision, the judges found Italy's highest court violated Germany's sovereignty by ruling in several Nazi crime compensation cases.
One of the cases involved a man who was deported to Germany in 1944 and forced to work as an enslaved laborer in a munitions factory.
The other cases concerned claims brought by the families of nine people who were among those killed by the German military in Civitella, Tuscany, in 1944. The massacre killed 203 civilians. The case sparked several other compensation claims.
Germany argues that it has already paid out billions of euros in compensation for atrocities committed by the Nazi regime since the end of WWII, taking part in extensive reparations and peace treaties with the countries affected.
The ICJ is the highest judicial organ of the United Nations, and its rulings are final and legally binding.